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                                                                    EXHIBIT 10.7

         THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
         NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933. THEY MAY NOT BE
         SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, OR OTHERWISE TRANSFERRED
         EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE
         SECURITIES ACT OF 1933, OR AN OPINION OF COUNSEL SATISFACTORY TO THE
         COMPANY THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT OR UNLESS SOLD
         PURSUANT TO RULE 144 UNDER SUCH ACT.

                        WARRANT TO PURCHASE COMMON STOCK
                        OF TOREADOR RESOURCES CORPORATION

WARRANT NO. 020                                      VOID AFTER JANUARY 15, 2008

                  This Warrant is issued to Barclays Bank PLC ("Holder") by
Toreador Resources Corporation, a Delaware corporation (the "Company"), on March
25, 2003 (the "Warrant Issue Date"). This Warrant is issued pursuant to the
terms of that certain Letter Agreement dated March 25, 2003, by and between the
Company, and Barclays Capital, an affiliate of the Holder.

                  1.       Purchase Shares. Subject to the terms and conditions
hereinafter set forth, the Holder is entitled, upon surrender of this Warrant at
the principal office of the Company (or at such other place as the Company shall
notify the holder hereof in writing), to purchase from the Company up to Ninety
Thousand (90,000) fully paid and nonassessable shares of Common Stock, par value
$0.15625, of the Company, as constituted on the Warrant Issue Date (the "Common
Stock"). The number of shares of Common Stock issuable pursuant to this Section
1 (the "Shares") shall be subject to adjustment pursuant to Section 7 hereof.

                  2.       Exercise Price. The purchase price for the Shares
shall be US$3.50 per share, as adjusted from time to time pursuant to Section 7
hereof (the "Exercise Price").

                  3.       Exercise Period. This Warrant shall be exercisable
commencing on the Warrant Issue Date and shall expire and be of no further force
or effect at 4:30 pm (Dallas time) on January 15, 2008 (the "Expiration Date").

                  4.       Method of Exercise. While this Warrant remains
outstanding and exercisable in accordance with Section 3 above, the Holder may
exercise, in whole or in part, the purchase rights evidenced hereby. Such
exercise shall be effected by:

                           (a)      the surrender of the Warrant, together with
a duly executed copy of the form of Notice of Election attached hereto, to the
Secretary of the Company at its principal office; and

                           (b)      the payment to the Company of an amount
equal to the aggregate Exercise Price for the number of Shares being purchased
by certified check or bank draft.

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                  5.       Certificates for Shares. Upon the exercise of the
purchase rights evidenced by this Warrant, one or more certificates for the
number of Shares so purchased shall be issued as soon as practicable thereafter
(with appropriate restrictive legends, if applicable), and in any event within
thirty (30) days of the delivery of the Notice of Election.

                  6.       Issuance of Shares. The Company covenants that the
Shares, when issued pursuant to the exercise of this Warrant, will be duly and
validly issued, fully paid and nonassessable.

                  7.       Adjustment of Exercise Price and Number of Shares.
The number of and kind of securities purchasable upon exercise of this Warrant
and the Exercise Price shall be subject to adjustment from time to time as
follows:

                           (a)      Subdivisions, Combinations and Other
Issuances. If the Company shall at any time prior to the expiration of this
Warrant subdivide its Common Stock, by split-up or otherwise, or combine its
Common Stock, or issue additional shares of its Common Stock as a dividend or
distribution with respect to any shares of its Common Stock, the number of
Shares issuable on the exercise of this Warrant shall forthwith be
proportionately increased in the case of a subdivision or stock dividend or
distribution, or proportionately decreased in the case of a combination.
Appropriate adjustments shall also be made to the purchase price payable per
share, but the aggregate purchase price payable for the total number of Shares
purchasable under this Warrant (as adjusted) shall remain the same. Any
adjustment under this Section 7(a) shall become effective at the close of
business on the date the subdivision or combination becomes effective, or as of
the record date of such dividend or distribution, or in the event that no record
date is fixed, upon the making of such dividend or distribution.

                           (b)      Reclassification, Reorganization and
Consolidation. In case of any reclassification, capital reorganization, or
change in the Common Stock of the Company (other than as a result of a
subdivision, combination, or stock dividend provided for in Section 7(a) above),
then, as a condition of such reclassification, reorganization, or change, lawful
provision shall be made, and duly executed documents evidencing the same from
the Company or its successor shall be delivered to the Holder, so that the
Holder shall have the right at any time prior to the expiration of this Warrant
to purchase, at a total price equal to that payable upon the exercise of this
Warrant, the kind and amount of shares of stock and other securities and
property receivable in connection with such reclassification, reorganization, or
change by a holder of the same number of shares of Common Stock as were
purchasable by the Holder immediately prior to such reclassification,
reorganization, or change. In any such case appropriate provisions shall be made
with respect to the rights and interest of the Holder so that the provisions
hereof shall thereafter be applicable with respect to any shares of stock or
other securities and property deliverable upon exercise hereof, and appropriate
adjustments shall be made to the purchase price per share payable hereunder,
provided the aggregate purchase price shall remain the same.

                           (c)      Carry Over of Adjustments. No adjustment of
the Exercise Price shall be made if the amount of such adjustment shall be less
than 1% of the Exercise Price in effect immediately prior to the event giving
rise to the adjustment, provided, however, that in such case any adjustment that
would otherwise be required then to be made shall be carried forward and shall
be

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made at the time of and together with the next subsequent adjustment which,
together with any adjustment so carried forward, shall amount to at least 1% of
the Exercise Price.

                           (d)      Discretionary Reduction in Exercise Price.
The Company may at any time or from time to time reduce the Exercise Price of
the Warrant.

                           (e)      Notice of Adjustment. Upon any adjustment of
the number of Shares and upon any adjustment of the Exercise Price, then and in
each such case the Company shall give written notice thereof to the Holder,
which notice shall state the Exercise Price and the number of Shares or other
securities subject to the unexercised Warrant resulting from such adjustment,
and shall set forth in reasonable detail the method of calculation and the facts
upon which such calculation is based. Upon the request of the Holder there shall
be transmitted promptly to the Holder a statement of the firm of independent
certified accountants retained to audit the financial statements of the Company
to the effect that such firm concurs in the Company's calculation of the change.

                           (f)      Other Notices. In case at any time prior to
the Expiration Date:

                                    (i)      the Company shall declare any
                                             dividend or distribution upon its
                                             shares of Common Stock payable in
                                             shares;

                                    (ii)     the Company shall offer for
                                             subscription pro rata to the
                                             holders of its shares of Common
                                             Stock any additional shares of any
                                             class or other rights;

                                    (iii)    there shall be any capital
                                             reorganization or reclassification
                                             of the capital stock of the
                                             Company, or consolidation,
                                             amalgamation or merger of the
                                             Company with, or sale of all or
                                             substantially all of its assets to,
                                             another corporation; or

                                    (iv)     there shall be a voluntary
                                             dissolution, liquidation or
                                             winding-up of the Company,

then, in any one or more of such cases, the Company shall give to the Holder (A)
at least 10 days' prior written notice of the date on which a record date shall
be taken for such dividend, distribution or subscription rights or for
determining rights to vote in respect of any such reorganization,
reclassification, consolidation, merger, amalgamation, sale, dissolution,
liquidation or winding-up and (B) in the case of any such reorganization,
reclassification, consolidation, merger, amalgamation, sale, dissolution,
liquidation or winding-up, at least 10 days' prior written notice of the date
when the same shall take place. Such notice in accordance with the foregoing
clause (A) shall also specify, in the case of any such dividend, distribution or
subscription rights, the date on which the holders of shares of Common Stock
shall be entitled thereto, and such notice in accordance with the foregoing
clause (B) shall also specify the date on which the holders of shares of Common
Stock shall be entitled to exchange their shares of Common Stock for securities
or other property deliverable upon such reorganization, reclassification,
consolidation, merger, amalgamation, sale, dissolution, liquidation or
winding-up, as the case may be.

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                           (g)      Shares to be Reserved. The Company will at
all times keep available, and reserve out of its authorized shares of Common
Stock, solely for the purpose of issue upon the exercise of the Warrant, such
number of Shares as shall then be issuable upon the exercise of the Warrant. The
Company will take all such actions as may be necessary to ensure that all such
Shares may be so issued without violation of any applicable requirements of any
exchange upon which the shares of Common Stock of the Company may be listed or
in respect of which the shares of Common Stock are qualified for unlisted
trading privileges. The Company will take all such actions as are within its
power to ensure that all such Shares may be so issued without violation of any
applicable law.

                  8.       No Fractional Shares or Scrip. No fractional shares
or scrip representing fractional shares shall be issued upon the exercise of
this Warrant, but in lieu of such fractional shares the Company shall make a
cash payment therefor on the basis of the Exercise Price then in effect.

                  9.       No Stockholder Rights. Prior to exercise of this
Warrant, the Holder shall not be entitled to any rights of a stockholder with
respect to the Shares, including (without limitation) the right to vote such
Shares, receive dividends or other distributions thereon, exercise preemptive
rights or be notified of stockholder meetings, and such holder shall not be
entitled to any notice or other communication concerning the business or affairs
of the Company. However, nothing in this Section 9 shall limit the right of the
Holder to be provided the Notices required under this Warrant.

                  10.      Participation in Rights Distribution. If at any time,
while this Warrant, or any portion thereof, is outstanding and unexpired, the
Company shall issue to all holders of its Common Stock rights (the "Rights")
entitling the holders thereof to purchase shares of Common Stock, the Company
also shall issue to the Holder identical Rights, with such number of Rights to
be issued to the Holder being based on the number of shares of Common Stock
which Holder would then be entitled to receive if this Warrant had been
exercised in full immediately prior to the issuance of the Rights. Prior to
issuing the Rights, the Company shall provide notice to the Holder as set forth
in Section 7(f). In connection with issuing the Rights, the Company will take
all necessary corporate action to at all times keep available and reserve out of
its authorized shares of Common Stock the number of shares of Common Stock
issuable upon exercise of the Rights.

                  11.      Transfers of Warrant. The Holder of the Warrants may
transfer this Warrant only in compliance with all applicable federal and state
securities laws; provided however, that this Warrant may only be transferred by
the Holder to a maximum of five individuals or entities. No subsequent transfer
of this Warrant by any assignee of the Holder shall be permissible, without the
prior written consent of the Company. In order for a transferee of this Warrant
to receive any of the benefits of such Warrant, the Company must have received
notice of such transfer, pursuant to Section 16 hereof, in the form of
assignment attached hereto, accompanied by an opinion of counsel, which opinion
shall be reasonably acceptable to the Company, that an exemption from
registration of this Warrant under the Securities Act of 1933, as amended, and
under any applicable state securities law is available.

                  12.      Replacement. Upon receipt of evidence satisfactory to
the Company of the loss, theft, destruction or mutilation of this Warrant and,
if requested by the Company, upon delivery of a bond of indemnity satisfactory
to the Company (or, in the case of mutilation, upon surrender of

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this Warrant), the Company will issue to the Holder a replacement warrant
(containing the same terms and conditions as this Warrant).

                  13.      Successors and Assigns. The terms and provisions of
this Warrant shall inure to the benefit of, and be binding upon, the Company and
the Holder hereof and their respective successors and permitted assigns as set
forth in Section 11.

                  14.      Amendments and Waivers. Any term of this Warrant may
be amended and the observance of any term of this Warrant may be waived (either
generally or in a particular instance and either retroactively or
prospectively), with the written consent of the Company and the Holder.

                  15.      Assumption of Warrant. If at any time, while this
Warrant, or any portion thereof, is outstanding and unexpired there shall be (A)
the acquisition of the Company by another entity by means of any transaction or
series of related transactions (including, without limitation, any
reorganization, merger or consolidation) that results in the transfer of fifty
percent (50%) or more of the outstanding voting power of the Company; or (B) a
sale of all or substantially all of the assets of the Company, then, as a part
of such acquisition, sale or transfer, lawful provision shall be made so that
the Holder shall thereafter be entitled to receive upon exercise of this
Warrant, during the period specified herein and upon payment of the Exercise
Price then in effect, the number of shares of stock or other securities or
property of the successor corporation resulting from such acquisition, sale or
transfer which a holder of the shares deliverable upon exercise of this Warrant
would have been entitled to receive in such acquisition, sale or transfer if
this Warrant had been exercised immediately before such acquisition, sale or
transfer, all subject to further adjustment as provided in this Section 15; and,
in any such case, appropriate adjustment (as determined by the Company's Board
of Directors in its sole discretion) shall be made in the application of the
provisions herein set forth with respect to the rights and interests thereafter
of the Holder to the end that the provisions set forth herein (including
provisions with respect to changes in and other adjustments of the number of
Warrant Shares the Holder is entitled to purchase) shall thereafter be
applicable, as nearly as possible, in relation to any shares of Common Stock or
other securities or other property thereafter deliverable upon the exercise of
this Warrant.

                  16.      Notices. All notices required under this Warrant
shall be deemed to have been given or made for all purposes (i) upon personal
delivery, (ii) upon confirmation receipt that the communication was successfully
sent to the applicable number if sent by facsimile; (iii) one day after being
sent, when sent by professional overnight courier service, or (iv) five days
after posting when sent by registered or certified mail. Notices to the Company
shall be sent to the principal office of the Company (or at such other place as
the Company shall notify the Holder hereof in writing). Notices to the Holder
shall be sent to the address of the Holder on the books of the Company (or at
such other place as the Holder shall notify the Company hereof in writing).

                  17.      Captions. The section and subsection headings of this
Warrant are inserted for convenience only and shall not constitute a part of
this Warrant in construing or interpreting any provision hereof.

                  18.      Governing Law. This Warrant shall be governed by the
laws of the State of Delaware.

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                  IN WITNESS WHEREOF, Toreador Resources Corporation caused this
Warrant to be executed by an officer thereunto duly authorized.

                                             TOREADOR RESOURCES CORPORATION

                                             By: /s/ DOUGLAS W. WEIR
                                                 -------------------------------
                                             Name: Douglas W. Weir
                                                   -----------------------------
                                             Title: Chief Financial Officer
                                                    ----------------------------

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                          FORM OF ELECTION TO EXERCISE

         The undersigned hereby irrevocable elects to exercise the number of
Warrants of TOREADOR RESOURCES CORPORATION set out below for the number of
Shares (or other property or securities subject thereto) as set forth below:

         (a)      Number of Shares to be Acquired:                    __________

         (b)      Exercise Price per Share:                           __________

         (c)      Aggregate Purchase Price [(a) multiplied by (b)]:   __________

and hereby tenders a certified check, bank draft or cash for such aggregate
purchase price, and directs such Shares to be registered and a certificate
therefore to be issued as directed below.

                           DATED this _______ day of ________________, _____.

                                       Per: ____________________________________

Direction as to Registration
Name of Registered Holder:          _____________________________________
Address of Registered Holder:       _____________________________________
                                    _____________________________________
                                    _____________________________________
                                    _____________________________________

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                               FORM OF ASSIGNMENT

             (To be executed by the registered holder if such holder
                        desires to transfer the Warrant.)

         FOR VALUE RECEIVED ______________________________ hereby sells, assigns
and transfers unto________________________ .

                  (Please print name and address of transferee)

this Warrant, together with all right, title and interest therein, and does
hereby irrevocably constitute and appoint ______________________________
Attorney, to transfer the within Warrant on the books of the within-named
Company, with full power of substitution.

Dated: __________________, 200_

                                 Signature_____________________________________
                                 (Signature must conform in all respect to name
                                 of holder as specified on the face of the
                                 Warrant.)

                                 ______________________________________________
                                 (Insert Social Security or Other Identifying
                                 Number of Holder)

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